Share Object data between two scenes, but no materials
Yes this can be done. First, you need to create the two scenes where the Object Data is linked, but the objects are not. After that, you can setup the materials in a way so they are different in both scenes.

Start off by creating the second scene using 'Link Object data'. This will copy the object, but link the mesh data. That means, when you edit a mesh in one scene, its shape updates in the other as well.



Blender allows you to choose if the materials are linked to your Object or the Object Data. By default it links to Data, that means that somewhere in the datablock where the mesh is stored, the information which face receives which material is stored as well. Since both scenes share the same mesh data, the materials would always be the same in both of them.



In your case, you will need to set the Link to Object instead, like in the screenshot here:



Now the information which face has which material is stored in the Object. Again, for the two scenes, the objects are different, only the data is shared.

Note that when you switch your material link from Data to Object, the material slot will be emptied. Click on this Icon to browse through a list of materials to link it back:



In your 'Blender Render' scene you can now assign completely different materials to the same mesh. However, keep in mind that if you delete a material slot, it will disappear in both scenes!